A logic/mathematical puzzle to start the New Year
Sunil Roy and I were strolling down the road – somewhere in Chelsea area with the rest of the family – when he posed an interesting puzzle for me. See if you can get it.
To give everybody a chance, refrain from posting the answer in the Comments section. Send me a personal message and I will put your name up if you solved it.
You have two dices. One has 1 thru 6 painted on its faces like a normal dice. The other has blank on every face. You can write down any integer number 1,2,3… on each of the blank faces of the second dice. You can even leave it blank – which would stand for 0. You are allowed to repeat the numbers (you can have two faces with the same number).
The question is: What numbers would you paint on the six faces of the second dice such that:
(*) When the two dice are rolled together, the sum total of the two faces up can be any integer between 1 and 12 AND
(*) The probability of any of those integers (meaning the sum of the two faces up being 1 or 2 or 3… or 12) is exactly the same.
You can assume that the two dices are unbiased. (It will be completely random which face will show up)